Method and apparatus for measuring acoustical impedances



March 10, 1931.

P. B FLANDERS 1,795,647

METHOD AND APPARATUS FOR MEASURING ACOUSTICAL IMPEDANCES Filed Feb. 19, 1929 2 Sheets-Sheet lwvawrop l? B. ICL-ANDEPS A 7" TOPNEY MPEDANCES March 10, 1931. P. B. FLANDERS METHOD AND APPARATUS FOR MEASURING ACOUSTICAL I Filed Feb. 19, 1929 2 Sheets-Sheet 2 lNVENTO/P B. IZANDERS ATTORNEY Patented Mar. 10, 1931 I PATENT orrlce UNITED STATES PAUL B. FLANDERS, OF EAST ORANGE, NEW JERSEY,

ASSIGNOR 'r o BELL TELEPHONE LABORATORIES, INCORPORATED, OF NEW YORK, N. Y'-, A CORPORATION OF NEW YORK METHOD AND APPARATUS FOR MEASURING- ACOUSTICAL IMPEDANGES Application filed February 19, 1929. Serial No. 341,268.

This invention relates tomethods of and apparatus for the measurement of acoustic impedance.

An object of the invention is to increase the precision with which the impedances of acoustic instruments, such as horns, can be measured, and to provide simple apparatus for this purpose.

By the acoustic impedance of a device, such as a horn, speaking tube, or other elements of a sound wave transmission system is meant the ratio of the sound Wave pressure at a given point to the volumetric displacement resulting therefrom over the cross section of the sound wave channel at that point. The acoustic impedance is in general a complex quantity, corresponding to the fact that the resistance to the wave motion comprises both dissipative and wattless components.

pedance acoustic line terminated by the device, and

comparing this pressure with the'pressure :known acoustic impedance.

The measuring apparatus is arranged to measure the ratio of the pressure at' the output' and of the line tothat at th and thus, in effect, to measure t drop between the ends of the line. Forasingle determination three pressure measurements in all are required, one with the deviceunder test connected to the acoustic line, and two additional measurements with difli'erent known impedances connected to the line.

It is a feature of the method of the inven-v tion that acoustic pressures only are meas- "ured.

Another feature of the invention is that the determination of the impedance value involves only the differences of direct indications corresponding to the pressure measurements; the determination of the absolute i5 value of the pressure is unnecessary. This is e pressure In accordance with the invention the imof an acoustic device is determined, by measuring the pressure at the end of an that obtains when the line is terminated by a input end,

, achieved by an arrangement of the apparatus whereby indications are obtained that are inversely proportional to the pressure.

Other features of the invention relate to the detail arrangements for producing, detecting and measuring the acoustic wave pressures. A constant wave pressure is obtained by means of an electrofmagnetic telephone receiver operating under constant current, and the pressures involved inthe impedance determinations are measured by means of a search tube and a condenser microphone or other suitable form of translating device. The pressures, which are detected by the electromotive forces they produce, are measured by balancing these electromotive forces in phase and amplitude against a constant reference E. M. F., this reference E. M. F. being proportional to the constant current in the driving receiver, and therefore to the constant impressed wave pressure.

Figs. 1, 2 and 3 illustrate diagrammatically the steps in themethod of measurement in accordance with the invention;

Fig. 4 illustrates schematically electrical circuit arrangements in accordance with the invention for detecting and measuring the acoustic wave pressures;

Fig. 5 shows a side elevation of a preferred form of the acoustical measuring apparatus of the invention, the electrical circuits being omitted. f

Fig. 6 shows a plan view of a portion of the same device taken below line 6-6; and

vFig. 7 illustrates an enlarged sectional view on line 7-7 of a portion of the device sholwing important elements. in greater detai Referring to Figs. 1, 2 and 3 which illustrate schematically the three steps in the method of measurement, the essential acoustic apparatus comprises a sound conduit 10, a source 11,- of sound waves connected to one end of the conduit, and a pressure measuring instrument 12, connected to the other end 00 by a short branch tube 13. At its output end the conduit is provided with means for connecting the device to be tested and the standard acoustic impedance devices used for comparison. The wave source 11 is preferably an electro-magnetic telephone receiver, the pressure of the sound wave generated being, in this type, proportional to the alternating electric current strength in the receiver winding. The pressure detecting instrument 12 is preferably a telephone transmitter of the electrostatic type, in which an E. M. F. is

connect the receiver 11 to a suitable source known impedance, the value placed by a of electrical currents and to an alternating current potentiometer circuit, to be described later, to which the transmitter 12 is also connected by leads 16 and 17.

In Fig. 1 a horn 18 is shown connected to the end of the sound conduit 10. This represents the device to be tested, or the unof which will be Z. In Fig. 2the horn is resolid plug 19, Which in effect provides an infinitely great impedance. The use of an infinite impedance for one of the standards of comparison simplifies the computation of the unknown impedance from the test observations, but is not essential to denoted by I I the method of the invention, the only requirethe formula ment being that two standards be used of difierent, known impedance values. In Fig. 3 an adjustable impedance standard is shown connected. This comprises a tube 20 in which a close fitting plunger'21 is adapted to slide, the position of the plunger being adjusted by means of a. rod 22. The acoustic impedance of this device depends upon the wave frequency and u on the length and cross sectional area 0 the "closed. conduit. Its value at ordinary room atmospheric conditions can-be calculated very accurately from where Z" denotes the impedance,

8, denotes the cross sectional area of the sound passage, 7, the sound wave frequency, 0, the velocity of sound in air, and Z, the length of the closed conduit.

Zis equal to the distancefrom the mouth of the tube to the face of the plunger 21, as indicated on the drawing.

The impedance Z is of non-dissipative character, that is, itis a substantially pure acoustic reactance, this being indicated by the operator 7' in Equation (1). The value of the impedance canrange from minus infinity to plus infinity, and can be adjusted to any desired value at a given frequency by varying -the length Z. The adjusting rod 22 may be graduated to indicate the units.

In accordance with vention' the length Z in suitable the method of the inpressures at the output end of the conduit 10 are measured in terms of the wave pressure generated by the receiver 11. The ratio of these pressures is the quantity actually measuredand, since a phase difierence is involved, the ratio is a complex quantity requiring for its determination the measurement of a real and an imaginary com-.

ponent. The complete measuring system is shown schematically in Fig. 4. The electrical circuits associated with the acoustic apparatus comprise a supply circuit and a balancing circuit, the pressure ratios being measured in the latter.

The supply circuit comprises a wave source 23 connected through a controlling resistance 24 to a wave filter 25, the purpose of which is to remove any harmonics that may be present in the generated wave. The output terminals of the filter are connected through transformer 26 to the leads 14 and 15 of the receiver 11. This transformer has two equal secondary windings, between which, with .their common point connected to ground, are

inserted equal resistances 27 and 28. The balanced arrangement thus provided prevents the flow of stray currents'to the receiver and alsoto the balancing circuit. Resistances 27 and 28 should be large in comparison with the electrical impedance of the receiver in order that thecurrent in'the receiver may be independent of variations in its impedance due to variations in the acoustic load thereon. Resistances 27 and 28 also serve as a means for obtaining an E. M. F. proportional to the generated sound wave pressure, since the latter 1s proportional to the current in the windings and, therefore, to the fall of potential across these resistances.- 4

The. balancing'circuit comprises a circuit 29, in which is included a telephone receiver 30, and branch circuits bymeans of which E. M. F.s proportional to the sound wave pressures are introduced. The E. M. F. proportional to the input sound pressure is introduced into 'circuit 29 through a circuit connected to the terminals of resistances 27 and 28 and including series resistances 31 and 32, reversing switch 33, shunt resistance 34, and shielded transformer 35.5 portional to the output sound Wave pressure is appliedto the balancing circuit through The E. M. F. pro-- in series with it tern.

amplifier 36 connected to leads 16 and 17 of the detecting transmitter 12, and thence through shielded transformer 37, series resistances 38 and 39 to a variable coupling impedance comprising a variable resistance 40 and a variocoupler 41. Resistances 38 and 39'are large in comparison with the coupling,

impedance in order hat the current in this part of the circuit may not beaifected by the adjustment of the latter during a test. The telephone receiver is coupled to circuit 29 through a shielded transformer 42 and has prising an inductance 43 in ser1es with a variable condenser 44. By means of the tuner the receiver circuit can be tuned to the test frequency thereby rendering it more sensitive and diminishing the general noise in the receiver. The use of shielded transformers and symmetrical circuits prevents the entrance into the receiver 30 of stray currents which would impair the -accuracy of the sysof the invention will be more The operation d from the following analyclearly understoo sis of the principles involved:

the receiver 11 depen at any actual generated pressure.

The ratio of the pressure at theoutput end of the sound conduit -10 to that generated by ds upon the value of the acoustic impedance in. which the conduit is terminated and also upon the wave transmission properties of the conduit itself together with the'acoustic impedance of the sound wave generator.

complicated since the conduit 1s a line having distributed mass and elastic constants, but, i

it may be shown that given frequency, the conduit and sound generator are equivalent to a simple impedance, the value of which can be added directly to that of the terminatin'g device, and a wave source the pressure of which .isrelated by aconstant factor to-the For a given tercoustic system may therefore mple ser1 'mination the a be regarded as a si rangement consisting of a pressure source, and two impedances, the wave motion therein being subject to the ordinary relationships between wave pressure and wave velocity.

Let. 1 and Z be the efiective input pressure and the equivalent impedanceof the conduit respectively, and let p p and p be the wave pressures at the output end when the conduit is terminated in the unknown impedance Z a tuning arrangement com-' These latter factors are somewhat es connected arwhere p p and From Equations an equation denote the ressure ratios. 3) and (4), y subtraction, for Z is obtained,

which when combined with Equation (1) In this equation Z 'is expressed interms of the known impedances Z differences of the pressure the known impedances is ma great, Z for example, Equ

The electrical portion of signed to give indications tional to the pressure ratios, it necessary to use only the di test observations in unknown impedance. solute magnitudes even the absolute tios, need not be values 0 determin and Z and of the ratios. If one of de infinitely ation becomes (7') thesystem is dedirectly proporthereby making iferences of the the computation of the The fact that the abof the wave pressures, or

f the pressure ra-- ed enables a high degree of precision to be attained.

It is to be noted involve the whichalso in also that against each other in the one related to the inp by a constant factor, and. from the output sound E. M. F.s are introducedinto the balancing circuit 29 in the manner already explained.

The E. M. F. corresponding is directly proportional to windings of the sound therefore to. the eife responding to the output first amplified to bring it to is then impresse ling devices 40, 41 Since 39 arelarge in comparison xvi ance of the coupling device,

this circuit is directly proporti put' sound pressure and is not appreciably affected by adjustments of the coupling def this current be denoted by I and the mutual impedance between the v above mentioned circuit and the balancing circuit be denoted by Z the vice. If the value 0 thereby 1n IZ papessur e difierences as: rat-10s, a 'es for accuracy. The determination of the pressure ratios is effected by the balancing of two E. M. Fls

ut sound pressure 1),,

generator 11, and ctive input pressure m The E. M. F. generated in transmitter '12,cor

d on the circuit composed of resistances 38 and 39 and the variable coupthe balancing circuit is equal to This E. M. F. canb'e varied in amplitude andin phase by adjustments of variable 131 Equations 6 and 7 I electrical circuit,

the other derived pressure. These to the sound input the'c'urrent in the sound pressure is ausable value and n5 resistances 38 and th the impedthe current in 1 20 onal to the out- E'. M. Fginduced i the coils of the resistance 40 and variocoupler 41, and thus can be made to balance the E. M. F. corresponding to input sound pressure. The balance condition, which is detected by the absence of tone in receiver 30, is represented by or k r m=;;-% (s) where E is the E. M. F. corresponding to the input sound pressure, is and is are constants relating the E. M' F. E and the current I to the corresponding sound pressures, and p denotes the output sound pressure for any given condition. The mutual impedance Z,,,, at balance, is thus proportional to the pressure ratio andis inversely proportional to the output pressure. If now the circuit is balanced successively with acoustic impedances Z Z and Z in accordance with the steps outlined above, corresponding values of the mutual impedance Z Z and Z will be found, which, when inserted in Equation (6) and (7) by means of Equation (8), give 1 ena -Z...) (2.1 Z...)

m1 m2) These equations, give the unknown acoustic impedance in terms of the known standards and of the differences of the mutual impedances in the balancing circuit.

The mutual impedance Z is made up of two components, a resistance 7", due to vari-- able resistance 40, and a reactance, 21rfM, due to the mutual inductance M between variocoupler 41. The dii ference of two mutual impedances is simply the difference of the resistance components a plus the difference of the reactances, as determined from the scale readings of the devices 40 and 41. It will be seen from a comparison of Equations 6 and 9, that the fact that the differences of the mutual impedances are alone involved follows from the fact that these impedances are inversely proportional to the output pressures, this being due to the arrangement of the circuits whereby the variable coupling device is operative upon the E. F. corresponding to the output pressure. Balancing could equally well be effected by inserting the variable coupling between transformer 35 and circuit 29, but this would lead to a more complicated expression for the unknown impedance, involving the absolute magnitudes of the pressure ratios, which are more difiicult to determine precisely.

The variable coupling device is limited in its range of adjustment of a phase change the conduit of 180, but this range may be effectively extended to 360 by means of reversing switch 33, which when operated changes the phase of the E. M. F. E by 180.

Figs. 5, 6, and 7, illustrate a preferred construction of the acoustic portion of the invention the apparatus bein arranged to facilitate the interchanging 0% the terminal impedances at the end of the sound conduit 10 in the course of a test. The elements comprising the sound generator 11, the sound conduit 10 and the pressure detector 12 are grouped together in a unit, which is pivotally mounted so that the sound conduit can be swung horizontally to engage successively the device to be tested and the impedance standards, these latter being mounted side by side on a fixed base which also carries the pivoted unit.

Referring to Figs. 5 and 6, which show respectivelya side elevation of the apparatus and a plan view of the portion to the right of line 66, base 45 carries, by means of brackets 46 a face-plate 47, adapted to receive the device to be tested and also the standards of acoustic impedance. A sub-base 48 pivotally mounted on 45 by stud bolt 49 and bushing 54, carries the sound conduit 10, sound source 11, and a coupling head 50 in which the pressure detector is mounted. The sound conduit is carried in pedestal bearings 51 which are provided with bushings 52 of sponge rubber or other sound absorbing material to prevent the transmission of sound vibrations from the walls of the conduit to the base. To prevent the transmission of vibrations along the walls of the conduit from the sound source, the conduit is divided into two parts which are coupled together by a piece of flexible rubber tubing 53. A sponge rubber cushion 65 supports the receiver and at the same time insulates it acoustically from the sub-base. A slide 55 attached to the base 45 supports the unbalanced weight at the receiver end of the sub-base.

The coupling head 50 is drilled through to continue the sound passage to its outer face with the same diameter as in the conduit 10. The outer face bears tightly against the rear face of plate 47 and is adapted to slide later ally thereover, both faces being cylindrically curved and centered on the axis of pivot 49 so that they remain in close engagement as the base 48 is rotated. Guides 56 attached to the top and bottom of plate 47 hold the end of in horizontal alignment. The faces of the plate 47 and the head 50 are kept in close engagement by curved clamping strips 57 which are pressed against flanges at the top an at the bottom of the head 50 by springs 58 which abut against inwardly pointing flanges on the guides 56. In Fig: 6 the upper guide plate has been removed to show more clearly the details of the coupling head and face plate, and in Fig. 7 an enlarged view of the section along the line 7--7, the construction of this portion is shown in greatcr' detail.

The face plate 4'7 is drilled with two horizontally spaced holes'of the same diameter as the sound passage in conduit 10 and at the same height above. base 45. One hole is adapted by screwed bushing 59 to receive the adjustable acoustic standard comprising tube 20, plug 21 and adjusting rod 22,- the outer end of the tube being supported from base 45 by bracket 60. The rod 22 is graduated to'indicate the effective length of the closed air column in the tube 20. The other hole is provided with a screwed bushing 61 to receive the device to be tested. The hole in this bushing and the corresponding aperture in the face plate is of thesame diameter as the main sound passage, but, as shown in Fig. 7

the face plate is deeply recessed so that when devices, having smaller-sound passages are to v be tested, special bushings or adapter's'can be of the recess provi of 61'to carry the smaller sound used in place almost to the face of coupling passage back head 50. p

The coupling head one of the bevelled sides having a threaded recess into which the shell of thepressure detecting transmitter 12 is screwed. From the centre of the base of the recess to a point in the main sound passage very close to the face of coupling head, a small hole less than one sixteenth of an inch transmit the wave pressure to the detector diaphragm.- A rubber washer 62, between the shell of the detecting transmitter and the base 'des an effective acoustic seal. The detecting transmitter preferably has a very small diameter, little more than an inch, to enable it to pling head and thereby to shortemthe length of the passage between it and'th main soun conduit. In its general construction it can follow the usual construction for electrostatic transmitters, the lack of sensitivity due to its small size being readily compensated by am- Guide pins 6d,

Stop pins 63 let into the curvedface of I plate 47 limit the travel bf the coupling head and facilitate the registering of the sound conduit '10 with the holes 1n the face plate. which loosely engage the clamping plates holes in the flanges, of guide plates 56 serve to hold the clamping plates in their proper position and to carry the clamping. springs 58. The electrical circuits are connected to leads 14,15, 16 and 17, which are'correspondingly numbered in Fig. 4. u

In making'a measurement with the device described above. the device to be tested is connected to the bushing 61, or to a suitable adapter, and the standard impedance is adjusted to a convenient finite value correspond- 50 has its sides bevelled,

in diameter is drilled to P be mounted in the cou- 57 and which fit tightly into in Equation (1) is equal to unity, since for this adjustment the impedance is least affected by errors in the setting. The length of the closed column is then equal to one eighth of the length of the sound wave. The soun conduit 10 is then turned to register with the device under test, an electrical balance is made inthe manner already described, and thecorresponding reading of the mutual impedance Z recorded. The sound conduit is next swung to a central position, the sound conduit being then completely closed by faceplate 457, thus giving an' infinite impedance termination. A second balance is efi'ected and thevmutual inductance Z g noted. A third balance is made with the soundconduit registering with the standard finite impedance, and the corresponding mutual inductance Z noted. The impedance of the device may then be computed fromEquation 10, the impedance Z being the acoustic impedance of the adjustable standard. 1

' What'is claimed is:

1. The method of measur ng the impedance ing the ratio of the pressure at the output end of a sound conduit to the pressure at the inut end when the conduit is terminated successivel'y by the device to be tested and by two known acoustic impedances of different values, the impedance of the said device, being computed from the difierences of the pressure ratios so obtained. i

2. The method in accordance with claim 1- which. includes the steps of producing electromotive forces proportional to said input ly and balancing said E. M. F.s against each other to ascertain the value of the pressure ratio. I p

3. The method in accordance with claim 1 which includes the steps of producing an E. M. F. bearing a second proportional to, the pressure 'at the output end, combining said E. M. F.s to produce an indication of their difference, and varyin said second E. M. F. in phase and in amplitu e to reduce the diiference to zerof.

of acoustic impedance devices of known impedance values and means for mounting a dea vice to be tested, and means for coupling the pressure respective- J I fixed relation to the pressure at the input end, of the conduit, producing a mounted thereon a plurality output end of said conduit acoustically to said known impedances and the device to be tested successively.

5.- Apparatus in accordance with claim 4 in 5 which the said member carrying the acoustic impedance standards comprises a cylindrically curved plate having horizontally spaced apertures for the attachment of the impedance devices, and in which the sound conduit w and the wave source are pivotally mounted whereby the coupling of the sound conduit to the several impedance devices is effected by rotating the sound conduit and the Wave source together with respect to said curved plate.

6. Apparatus in accordance with claim 4 in which one of the known impedance devices comprises a closure for the output end of said conduit, corresponding to an infinitely great acoustic impedance, and in which another of the known impedance devices comprises a closed tube in which the length of the enclosed air column is adj ustablej 7. Apparatus 'for the measurement of acoustical impedance comprising a sound conduit, a sound wave source coupled to the input end of said conduit, means for measuring the ratio of the wave pressure impressed upon said conduit by said source to the wave pressure at the output end of said conduit and means for coupling the output end of said conduit successively to a plurality of acoustical impedance devices including the device to be tested. In witness whereof I hereunto subscribe my name this 15th day of February, 1929.

. PAUL B. FLANDERS.

lit? 

